Jury simulation using SimPy
In this article we design and build a SimPy simulation model of a jury summoning process The goal is to reduce the number of people summoned for jury service.
Simulation is often seen as an easy way to model to situation. It is not. This model highlights a key lesson for simulation modelling in general: details matter, sometimes a lot.
#orms #Python
https://www.solvermax.com/blog/jury-simulation-using-simpy
Efficient jury empanelling: Respecting people's time
This article is inspired by a recent experience of being summoned for jury service. We describe a simulation model of the jury selection process. The goal is to explore how the needs of the justice system can be met while also respecting the time of people who report for jury service. Specifically, we want to see if the number of people summoned can be reduced while ensuring that sufficient people are available for the scheduled trials.
Jury service is an important civic duty, providing a way for people to directly participate in upholding the law and contribute to their community. But the jury service process, like much of the justice system, is designed around the needs of the system rather than the needs of the people it serves.
#orms #Python
https://www.solvermax.com/blog/efficient-jury-empanelling-respecting-peoples-time
The muffin problem: A slice of recreational maths
In this article, we solve 'The Muffin Problem' which is a recreational maths puzzle that is simple to state but hard to solve in general.
The goal of the muffin problem is to divide a number of muffins equally between a number of students, maximizing the size of the smallest piece that any student receives. Some cases are trivial, while some others are easy. But once we have more than a few muffins and/or students, this becomes a difficult problem to solve.
We use a Mixed Integer Linear Program to solve the problem. Along the way we play with some parallel computing to substantially reduce the run time, and throw in some symmetry-breaking constraints and objective function bounds to help the solver.
#orms #Python
https://www.solvermax.com/blog/the-muffin-problem-a-slice-of-recreational-maths
Pivot irrigators in a 100 acre field
We formulate a non-linear, non-convex model for optimizing the layout of centre-pivot irrigators in a field. Several free and commercial solvers fail to find good solutions. Then we try the MINLP-BB solver via NEOS using a multi-start technique.
Can it find an optimal solution?
#python #orms
https://www.solvermax.com/blog/pivot-irrigators-in-a-100-acre-field
Locational marginal pricing of potatoes
We apply Locational Marginal Pricing (LMP) to the supply of potatoes. The article describes the model, calculation of LMPs, and scenarios for how the suppliers and contractors may respond to the price signals.
#orms #pyomo
https://www.solvermax.com/blog/locational-marginal-pricing-of-potatoes
Permission granted: A role mining model
We implement a recently published role mining model using both constraint programming and mixed integer linear programming, then compare their relative performance while solving several examples.
https://www.solvermax.com/blog/permission-granted-a-role-mining-model
#orms #pyomo #ortools #python
New item in our list of #orms resources:
Collection of videos from Associate Professor Alberto Del Pia, University of Wisconsin-Madison.
There are around 100 videos, collated into playlists relating to specific optimization papers taught at the university.
https://www.solvermax.com/resources/links/online-courses/optimization-nation
Optimal rational approximation using SciPy
In this article we solve a non-linear curve fitting problem using the SciPy library. SciPy is especially well-suiting to solving this type of problem, as it includes a variety of functions for fitting and optimizing non-linear functions.
Along the way, we illustrate how to use SciPy's curve_fit and minimize functions for this type of task. In addition, we look at some good practices to apply when solving this type of problem.
#python #scipy #orms
https://www.solvermax.com/blog/optimal-rational-approximation-using-scipy
Article: Can AI code an entire optimization model?
In this article we pursue an ambitious goal: Create an entire, non-trivial optimization model using Artificial Intelligence (AI).
Our approach mimics a user who is familiar with the situation, and has some experience with formulating optimization models, but is not familiar with implementing an optimization model in Python code. We want the AI to do all the coding for us.
We report our experience of using Copilot to write a model for us. Rather than presenting a verbatim transcript, which is very long, we focus on what went well and what didn't go well as the model evolves. We also summarize general lessons from the process.
https://www.solvermax.com/blog/can-ai-code-an-entire-optimization-model
Article: Objectives matter: Sorting using a MIP model
We replicate a model by Erwin Kalvelagen at Yet Another Math Programming Consultant (YAMPC), "Sorting using a MIP model".
In this article, we assess the impact of using an alternative objective function in the same model. The idea is to give the HiGHS solver greater traction while working through the solution space, hopefully helping it to solve the model faster. We've found this technique to be useful for some other models – will it help in this situation?
https://www.solvermax.com/blog/objectives-matter-sorting-using-a-mip-model
#Python #orms #optimization #modelling #CPLEX #highs
Article: Gerrymandering made easy
In this article, we take a simple approach to modifying a redistricting design. We add a requirement to our model that could be interpreted as either:
- The laudable goal of grouping together "communities of interest" – a common requirement when designing voting districts; or
- A nefarious attempt to manipulate the electoral outcome by gerrymandering.
Gerrymandering is the opposite of the model's purpose in our previous article. But, as model designers, we need to be aware that we don't always control the purposes to which decision makers apply our models and decision makers don't always understand the implications of small changes to a model.
https://www.solvermax.com/blog/gerrymandering-made-easy
#Python #orms #optimization #modelling #gurobi #highs
@AustinLBuchanan
Article: Academics, please publish your data and code
Academic research papers can be a valuable source of material for creating and improving real world optimization models. But we wish that academics would publish working code and data to accompany their papers.
In this article:
- Firstly, we briefly look at some reasons why academics might be reluctant to publish their data and code.
- Then we replicate, modify, and explore a published model that has been done well, with the data and program code publicly available.
https://www.solvermax.com/blog/academics-please-publish-your-data-and-code
#Python #orms #optimization #modelling #gurobi #highs
@AustinLBuchanan
Article: Well, that escalated quickly: Pyomo
We conclude our series of articles to decide the best order for positioning devices in a rack.
This article discusses Model 5, which formulates the situation in Pyomo as a Mixed Integer Linear Program (MILP). We solve the model using a single instance of Gurobi and parallel instances of the HiGHS solver.
Does this model perform better than the previous methods?
https://www.solvermax.com/blog/well-that-escalated-quickly-pyomo
#Python #orms #optimization #modelling #gurobi #highs
Article: Well, that escalated quickly: OR-Tools
In this series of articles, we look at a simple optimization situation that requires deciding the best order for positioning devices in a rack.
This article discusses Model 4, which formulates the situation as a Constraint Programming problem and solves it using the CP-SAT solver in OR-Tools. Does it perform better than the previous methods?
https://www.solvermax.com/blog/well-that-escalated-quickly-or-tools
#Python #orms #optimization #modelling #ortools
Article: Well, that escalated quickly: Local search
In this series of articles, we look at a simple optimization situation that requires deciding the best order for positioning devices in a rack.
This article discusses Model 3, which uses a local search heuristic running in parallel. Does it perform better than the previous enumeration and random search methods?
https://www.solvermax.com/blog/well-that-escalated-quickly-local-search
#Python #orms #optimization #modelling
Article: Well, that escalated quickly: Random search
In this series of articles, we look at a simple optimization situation that requires deciding the best order for positioning devices in a rack.
This article discusses Model 2, which uses a random search method running in parallel. Does it perform better than the enumeration method of Model 1?
Along the way, we asked Claude AI to help with some of the programming. Claude was useful, though the experience was somewhat mixed.
https://www.solvermax.com/blog/well-that-escalated-quickly-random-search
#Python #pyomo #orms #optimization #modelling #ClaudeAI
Article: Well, that escalated quickly: Enumeration
In this series of articles, we look at a simple situation that requires deciding the best order for positioning devices in a rack. We use four methods for solving this problem:
- Model 1. Enumerate all possible position orders.
- Model 2. Search randomly for a specified time.
- Model 3. Constraint programming using OR-Tools.
- Model 4. Mixed integer linear programming using Pyomo.
Along the way, we see how a problem's size can quickly escalate to a colossal magnitude. We also demonstrate how, contrary to popular belief, that magnitude is not necessarily a barrier to finding a good solution.
We start with Model 1. The other models will follow.
https://www.solvermax.com/blog/well-that-escalated-quickly-enumeration
#Python #pyomo #orms #optimization #modelling
In this article series, we look at improving the efficiency of a pallet warehouse, where all items are stored on standard-size pallets.
Along the way, we:
- Formulate a non-linear model of the situation.
- Compare several solvers, to see how they perform.
- Linearize our model to, hopefully, make it easier to solve.
- Disaggregate our model to make some variables exogenous, then iterate over an enumeration of the exogenous variables.
- Demonstrate use of Pyomo's last() and next() functions, which enable us to work with elements of ordered sets.
- Turn off a constraint using Pyomo's deactivate() function.
Importantly, we show that there's a surprising amount of extra storage space available for free, or minimal cost, just by redesigning the warehouse's racks and shelves.
The model is built in Python using Pyomo.
https://www.solvermax.com/blog/warehouse-space-for-free-non-linear-model
Blog: Python embedded in Excel: First impressions
Microsoft recently announced a new Excel feature, Python embedded within Excel. This is great news, as it combines our two favourite tools: Excel and Python.
Since our focus is on optimization modelling, we immediately wondered if it is possible to use a Python library to solve optimization models directly within Excel. Spoiler alert, it is!
In this article, we experiment with building and solving a linear program in Excel using the Python SciPy library.
#Excel #Python #SciPy #optimization #orms
https://www.solvermax.com/blog/python-embedded-in-excel-first-impressions
New section on our sister website:
Spreadsheet good practice guidelines
https://www.i-nth.com/blog/introducing-our-spreadsheet-good-practice-guidelines
Currently in the early stages of development, so very much a work in progress. Comments welcome.
#Excel
